So consider the classic metric space \\( \\{A,B,C, D\\} \\) with d (x,y)= if x = y then 0 else 1, and the pair f = rotate obj clock wise, and g flip A with B.

Hmm. Now what i actually meant to mean was that there are no adjunct f and g that are not inverses. And i do think that is true, but am not sure.